THERMAL EMISS1YITY OF THIN WIRES IN AIR. 
401 
F (t) is the resistance in ohms of this 17‘07 centims. of this 6-mil wire at any 
particular temperature, t. Now, when A equals 1'4 ampere, and d equals 
0-152 millim., and l is 17’07 centims., 
KA 2 4 x 9-858 , 
- - — = 14.91-7 ; 
l 7r cV 
therefore, the equation (9) becomes 
£' 3 = 2587-4 (t - 12) xjj(t) - 14917 F («).(10). 
To obtain a curve representing the first term on the right-hand side of this equation, 
the curve for $ (t), given for the 6-mil wire in fig. 11, was altered by simple geo¬ 
metrical construction so as to give a curve for t X xp ( t ). The ordinates of this curve 
were then altered, graphically, so as to give to a convenient, scale a curve for 
2587*4 t . xp (t), and, lastly, the ordinates of this curve were reduced, graphically, in 
the proportion of £ — 12 to t. 
To obtain the curve representing the second term on the right-hand side of equation 
(10), the ordinates of the curve on fig. 14 were multiplied by 1491 "7, and then the 
curve was re-drawn to the same scale as the curve representing 2587‘4 (t — 12) xp (t). 
The ordinates of the two curves were then subtracted from one another, and a curve, 
having for its ordinates the difference of the ordinates of the last two curves, was 
drawn, which gives the values of dHjdx 3 for any value of t. This curve is seen 
in fig. 15 (Plate 15), it is parabolic in shape, cuts the axis along which temperature is 
reckoned at t equals 315° C.,and has its vertex approximately in the line along which 
dHjdx 2 is reckoned. 
A similar investigation was made for the same wire for a current of 0'6 ampere, and 
it was found that the curve for dHjdx* in this case cut the axis of temperature at 
60°-3 C. 
The fact that dHjdx 2 is nought at a particular temperature tells us, of course, 
mathematically nothing about the actual value of dtjdx, but from our general know¬ 
ledge of temperature curves, we know that when a current is passing through a fine 
wire, as in our experiments, the temperature will rise rapidly along the wire in the 
neighbourhood of the supports, then rise more slowly, and at no great distance from 
the supports the temperature curve will become nearly flat, and will be absolutely flat 
over the middle portion of the wire. 
We are, therefore, justified in assuming that dHjdx 1 and dtjdx are nought at about 
the same point of the wire. 
On examining the numbers in Table V., which refer to the 6-mil wire, it will be 
noticed that the mean temperatures of the wire for currents of 1*4 and 0'6 ampere 
respectively, were 314° C. and 60°"2 C., which are almost exactly the temperatures 
MDCCCXCII.—A. 3 F 
